Question

4.8. The objective is to estimate the total of the variable CS82 (= y) for the MU284 population. Two-stage sampling is used, with SI sampling of $n_1 = 5$ from $N_1 = 50$ PSUs. The PSUs are the clusters defined in Appendix C. In every selected PSU, an SI sample of size $n_2 = 2$ is drawn. The following results were recorded: i $N_i$ k $y_k$ 11 6 61 8 58 10 5 5 24 13 23 12 20 5 113 11 112 8 48 5 266 2 270 7 14 7 77 16 81 10 (a) Compute an unbiased estimate of the total of the variable CS82. (b) Compute unbiased estimates of $V_{PSU}$, $V_{SSU}$, and $V = V_{PSU} + V_{SSU}$. Also, compute the corresponding cve. (c) Compute simplified variance estimates according to equations (4.6.1) and (4.6.2), as well as the corresponding cves. Comment on your conclusions.

          4.8. The objective is to estimate the total of the variable CS82 (= y) for the MU284 population. Two-stage sampling is used, with SI sampling of $n_1 = 5$ from $N_1 = 50$ PSUs. The PSUs are the clusters defined in Appendix C. In every selected PSU, an SI sample of size $n_2 = 2$ is drawn. The following results were recorded:

i   $N_i$   k   $y_k$
11  6   61  8
    58  10
5   5   24  13
    23  12
20  5   113 11
    112 8
48  5   266 2
    270 7
14  7   77  16
    81  10

(a) Compute an unbiased estimate of the total of the variable CS82. (b) Compute unbiased estimates of $V_{PSU}$, $V_{SSU}$, and $V = V_{PSU} + V_{SSU}$. Also, compute the corresponding cve. (c) Compute simplified variance estimates according to equations (4.6.1) and (4.6.2), as well as the corresponding cves. Comment on your conclusions.

48 the objective is to estimate the total of the variable cs82 y for the mu284 population two stage sampling is used with si sampling of n1 5 from n1 50 psus the psus are the clusters defi 48364

Added by Ronnie B.

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